Using elementary transformations, find the inverse of each of the matrices, if it exists.
$$
\left[\begin{array}{rr}
2 & -3 \\
-1 & 2
\end{array}\right]
$$

Answer

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Algebra

NCERT Class 12 Part 1 - Math

Chapter 3

Matrices

Section 4

Operations on Matrices

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Video Transcript

In the question, we have to use the elementary transformation for finding the universe for the government metrics. That the matrix is the matrix with element 3 -1 -4. To Now moving towards the solution, like these metrics be represented by a. So it will be called to the metrics with elementary -1 -4 to now, as we know that we can represent this A metrics as a equals to the identity matrix into the A. So it will be written us three minus one minus 42 is close to the identity matrix which is 1001 into a. Now moving further, this will be right on us minus 11 -4, 2 is close to one, into way if you add your are one with our two. So It will now be written as 1 -1 -4, two. is the calls to 1 -1 01 into way if you make your R1 as -1 into our one. So now it will be written as one minus 10 minus two equals two minus one minus one minus four minus three into a if you ag 4/4 4 times of our one and art that is your heart, you will become our two plus four times so far one. Now moving for that It will be four. Then return as 1 -101 is equal to minus one minus 12 three by two In two way. If you multiply your R two by minus one by two that is your R two will become minus one by two in too hard to Now this will be returned as 1001 is according to one, x 2-3 x two in the way if you act your are too in our one that is our one will become our one plus R two. So from here you're a inverse will be equal to the metrics with the element 11 by 2 to 3 by two. Thank you.

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